NEW TYPE OF MULTI-DEGREE-OF-FREEDOM

PIEZOELECTRIC ACTUATORS, BASED ON ACTIVE

KINEMATIC PAIRS

Ramutis Bansevicius, Arunas Lipnickas

Kaunas University of Technology, The Mechatronics Center for Research, Studies and Information

Kestucio 27, Kaunas, Lithuania

Minvydas Ragulskis

Kaunas University of Technology, Research Group for Mathematical and Numerical Analysis of Dynamical Systems

Studentu 50-222, Kaunas, Lithuania

Keywords: Mechatronics, Piezoelectric Actuators, Active Kinematic, Active Bearing, Modelling.

Abstract: New type of multi-degree-of-freedom piezoelectric actuators based on active kinematic pairs is presented.

The contact zone of this type of actuator is formed by two oscillating transducers in a form of rod, plate,

disk or cylinder. Depending on a phase of both transducers in a contact zone and their amplitudes, either

high frequency oblique impacts or periodic change of normal reaction in the contact zone are generated,

leading to continuous motion of one of the links. Schematics of piezoelectric motors, using two active

elements in the contact zone and comprising the number of degrees-of-freedom up to 5 are presented.

Several applications for laser beam deflection and positioning devices in the plane are considered. The

concept of active bearing is introduced; this type of support has no processing datum surface errors.

1 INTRODUCTION

It is worthwhile to introduce the concept of active

kinematic pair in the design of multi-degree-of-

freedom actuators and 3D positioning systems. Such

concept is especially useful in the design of adaptive

positioning systems (Ragulskis, 1988; Bansevicius,

2002a). The characteristic feature of active

kinematic pair is that one or both elements of it are

manufactured from active or smart materials such as

piezoelectric, magnetostrictic or shape memory

materials (Bansevicius, 2002a). Active kinematic

pair can change its kinematic structure or parameters

depending on external conditions or excitation

characteristics (Bansevicius, 2002b). The multi-

functionality of the mechanisms can be achieved

applying direct or inverse piezoelectric effects. In

other words, several different functionalities as

motion generation, measurement of parameters of

motion, control of friction forces in the contact zone

can be implemented into one instrument

(Bansevicius, 2000a; Ko and Kimb, 2006, Chu and

Fan, 2006). Excitation of static or quasi-static

deformations, multi-directional and multi-shape

resonance oscillations, generation of motion in the

contact zone, transformation of oscillations into

continuous motion are just several examples of

application of active kinematic pairs (Bansevicius,

2000b; Bansevicius and Ahmed, 2000ab;

Bansevicius, 2001).

Active kinematic pairs enable:

• Control of the number of degrees-of-freedom of

the kinematic pair by means of friction force

control in the contact zone or generation static

or quasi-static deformations of the element of

the pair;

• Generate forces and moments in the contact

zones;

• To effect additional functions – self-

diagnostics, multi-functionality, adaptively,

self-assembly;

• To implement two levels of degree-of-freedom.

The first level comprises large deflections or

displacements, produced by transformation of

159

Bansevicius R., Lipnickas A. and Ragulskis M. (2009).

NEW TYPE OF MULTI-DEGREE-OF-FREEDOM PIEZOELECTRIC ACTUATORS, BASED ON ACTIVE KINEMATIC PAIRS.

In Proceedings of the 6th International Conference on Informatics in Control, Automation and Robotics - Robotics and Automation, pages 159-164

DOI: 10.5220/0002180401590164

 SciTePress

resonance oscillations of pair’s links into

continuous motion. The second level deals with

small displacements (in nanometre range),

implemented by means of direct piezoelectric

effect and specific sectioning of electrodes.

2 TWO ACTIVE ELEMENTS IN

THE CONTACT ZONE

Applying two active elements in the contact zone of

piezoactuator enables enlargement of the generated

force or torque and transforming oscillations into

continuous motion. High frequency oblique impacts

are generated in the contact zone between two rod

type transducers (Fig. 1). Only longitudinal

resonance oscillations are generated in these rods.

Specific phase differences between the oscillations

in these rods enable variation of the continuous

motion parameters. Zero phase difference generates

direct continuous motion, 180 degree phase

difference enables reverse continuous motion. Phase

difference between 0 and 90 degrees (or between

180 and 270 degrees) changes the normal force

component in the contact zone and helps to tune

dynamical parameters of the whole system with the

rheological parameters of the contact zone.

Figure 1: Piezoelectric motor. 1 – the first piezoelectric

transducer (slider); 2 – contact element; 3 – the second

piezoelectric transducer (active support); 4 – spring.

Several schematics of such piezomotors are

presented in Figures 2, 4 and 6. Symmetric scheme

(Fig. 2) enables sufficient increase of the generated

force. Combination of different Eigen modes helps

to achieve larger deflections or displacements of the

sliding element. It must be noted that the reverse

mode is symmetric in all schemes and can be

realised by altering the phase of one of the

transducers by 180 degrees. The scheme presented

in Fig. 2b is implemented in the design of miniature

longitudinal small stroke (2 mm) piezomotor and

well illustrates the technological advantages of such

an approach.

Figure 2: Two cases of piezoelectric motors with two

active elements in the contact zone: (a) - symmetric

scheme; only longitudinal first Eigen shape resonance

vibrations are generated in all actuators (the node is

located in the middle point of the actuator); (b) -

application of different Eigen shapes to increase the

stroke: longitudinal resonance oscillations (second Eigen

shape) are excited in the slider (two nodal points);

longitudinal resonance oscillations (first Eigen shape) are

excited in the supporting actuator (one nodal point).

2.1 Numerical Analysis of Active

Kinematic Pair comprising Two

Active Elements in the Contact

Zone

The active kinematic pair shown in Fig. 1 is

modelled using finite element techniques

(Zienkiewitcz and Taylor, 1991). We used hybrid

elastic body – piezoelectric material finite element

formulations, described in (Ragulskis, 1998). Non-

adaptive uniform finite element meshes were used

for the slider and the active support in order to

secure the best stability and convergence of the

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numerical solution, while an adaptive mesh was

used for the contact element (Fig. 1).

The effect of the pressing spring was assumed as

constant forces, acting to nodes of the outside

surface of the contact element. Limiters for the slider

were modelled as kinematic constrains for the nodes

of the external surface of the slider, permitting

longitudinal but impeding transverse displacements.

Eigen shapes of the slider and the contacting

element were calculated. Then the electrical

excitation of the piezoelectric material was selected

in such a way that the oscillations of the slider and

the active support element would follow their Eigen

shapes (and resonance Eigen frequencies) as close as

possible.

The time step was selected to accommodate

accurate integration of the fifteenth Eigen mode (the

first fifteen Eigen modes were sufficient to represent

complex dynamical processes taking even in the

contact zone). Schematically, the piezoelectric

excitation can be represented as:

()

(

)

()

(

ϕωδδ

)

+Φ=

Φ=

tyxjiF

jiAA

jiSS

sin,,

(1)

where is a matrix of dynamical forces acting to

the nodes of the slider; are forced acting to the

nodes of the active support; and are first

Eigen shapes of the slider and the active support

(Eigen shape depends from the allocation of

electrodes);

is the resonance frequency (both for

the slider and the active support);

is the phase

difference of the electric excitation. Numerical

simulations produce a large dataset of results. Only

the trajectory of the middle contact point of the

slider is shown in Fig. 3 in the x-y phase plane in

order to represent main dynamical features.

It can be seen that optimal longitudinal motion of

the slider is achieved at

= 0, or

= 180 (the

reverse mode). Other phase differences result into

chattering mode when the oblique impact energy is

not optimally transferred into the continuous

longitudinal motion of the slider.

(a)

(b)

(c)

(d)

Figure 3: Numerically reconstructed transient dynamical

processes taking place at different phases: (a)

= 0; (b)

= 90; (c)

= 180; (d)

= 270 degrees. Note different

scales of x-axis.

NEW TYPE OF MULTI-DEGREE-OF-FREEDOM PIEZOELECTRIC ACTUATORS, BASED ON ACTIVE

KINEMATIC PAIRS

161

3 APPLICATIONS OF MULTI-

DEGREE-OF-FREEDOM

PIEZOELECTRIC ACTUATORS

Piezoelectric actuators based on active kinematic

pairs enable realisation of different types of motion.

Schematic of piezoelectric rotary motor is presented

in Fig. 4. Dynamical processes taking place in the

contact zone are analogous to the basic type

mechanism shown in Fig. 1 and depend on the phase

difference and rheological properties of the contact

surfaces. As in the previous schemes, the resonance

frequencies of the radial oscillations of the disk type

transducer and longitudinal oscillations of the rod

piezotransducer can differ in the range of few

percents. In fact, the range of tolerable differences

depends on the damping in the transducers and in the

whole system in general.

Figure 4: Increasing the velocity by using bimorphic

transducers. 1, 2 – bimorphic piezotransducers; 3 – spring;

4 – schematics of the electrodes; 5 – excitation wiring

diagram; H – poling vector.

Figure 5: Schematics of angular motion piezomotors with

increased torque. 1 – piezoceramic ring; 2 – fixing

element; 3 – rod type piezotransducer; 4 – spring.

Figure 6: Schematic diagram of translational motion

piezomotor analogous to symmetric scheme presented in

Fig. 4.

Two new instrumentation schemes shown in Fig.

7 and Fig. 8 have been implemented practically.

Initial experiments have shown their effectiveness

for implementation small one-degree-of-freedom

positioning systems dedicated for precision

instrumentation. Such schemes can be easily

manufactured using low cost piezotransducers.

Piezomotors with two active elements in the

contact zone can be effectively applied in the design

of optical beam reflection and scanning equipment.

Two cases of such instrumentation are presented in

Fig. 9 and 10. Oblique high frequency impacts are

generated in the contact zone between the cylinder

section and rod type transducer (Fig. 9).

The scheme showed in Fig. 10 enables

implementation of two-degrees-of-freedom motion

of the mirror by electric control of different disk or

plate type piezotransducers’ electrodes.

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Figure 7: Schematics of translational motion piezomotors

with two active elements in the contact zone. (a): 1 –

piezoceramic transducer (longitudinal resonance second

Eigen shape oscillations; two nodal points); 2 –

piezoceramic bimorphic bending resonance oscillation

transducer (first Eigen shape; two nodal points). (b): 3 –

longitudinal vibration transducer (first Eigen shape; one

nodal point); 4 – bending vibration transducer (second

Eigen shape; three nodal points).

Figure 8: Symmetric translational motion piezomotor with

two active elements in the contact zone. (a): sectioning of

the electrodes; (b): 1, 2 –longitudinal resonance

oscillations (first Eigen shape) and in-plane bending

oscillations (second Eigen shape) are generated in two

identical piezotransducers.

Figure 9: Optical beam reflector. 1 – mirror; 2 – fixing

elements; 3 – piezoceramic sector; 4 – piezoelectric rod,

generating longitudinal resonance first Eigen shape

oscillations.

NEW TYPE OF MULTI-DEGREE-OF-FREEDOM PIEZOELECTRIC ACTUATORS, BASED ON ACTIVE

KINEMATIC PAIRS

163

Figure 10: Two-degree-of-freedom optical beam

reflector/scanner. 1 – mirror; 2 – segment of spherical

piezotransducer; 3 – fixing element (scheme is not

specified); 4 – plate type piezotransducer; 5…12 –

sectioned electrodes.

4 CONCLUSIONS

New type of multi-degree-of-freedom piezoelectric

actuators, based on active kinematic pairs, is

presented in this paper. Schematics of piezoelectric

motors, using two active elements in the contact

zone and comprising the number of degrees-of-

freedom up to 5 are presented. Several applications

for laser beam deflection and positioning devices in

the plane are described. The concept of active

bearing is introduced.

The contact zones of these actuators are formed

by oscillating pairs of piezoelectric transducers.

Control of the phase difference between the

transducers enable transformation of oblique impacts

into continuous motion. Such types of actuators are

characterised by high resolution, low time constant,

and are applicable in different areas of precision

mechatronics.

ACKNOWLEDGEMENTS

Research has been financed by Lithuanian State

Science and Studies Foundation (High-Tech

Development program’s research project

PjezoAdapt).

REFERENCES

Ragulskis, K., et al., 1988, Vibromotors for Precision

Microrobots, Hemisphere Publishing Corp., New

York, 310 p.

Bansevicius, R. et al., 2002a, The Mechatronics

Handbook, CRC Press, Boca Raton.

Bansevicius, R., 2002b, Latest trends in the development

of piezoelectric multi-degree-of-freedom actuators/

sensors. Responsive systems for active vibration

control, NATO Science Series, Vol. 85, Kluwer

Academic Publishers, Dordrecht, p.207-238.

Bansevicius, R., et al., B., 2000a, Design and control of

precise robots with active and passive kinematic pairs,

Mechatronics 2000: Proceedings of the 7-th

Mechatronics Forum, Atlanta, Georgia, U.S.A.,

Pergamon, p.10-16.

Ko, H-P., et al., 2006, A novelty in ultrasonic linear motor

using the radial mode of a bimorph, Sensors and

Actuators A 125, p.477–481.

Chu, C-L. and Fan, S-H., 2006, A novel long-travel

piezoelectric-driven linear nanopositioning stage,

Precision Engineering 30, p.85–95.

Bansevicius, R., et al., 2000b, Active error compensation

for precise machines, IMEKO 2000: XVI IMEKO

World Congress Proceedings, Vienna, Vol. 8, p.21-26.

Bansevicius, R. and Ahmed, S., 2000a, Piezoelectric

Active Supports, U.K. Patent 2313982, Patented by

Smart Technology Ltd., U.K..

Bansevicius, R. and Ahmed, S., 2000b, Piezoelectric

Actuators, U.K. Patent 2332090, Patented by Smart

Technology Ltd., U.K..

Bansevicius, R. and Ahmed, S., 2001, Bearings and

Support, USA Patent 62625114B1, Patented by Smart

Technology Ltd., U.K..

Zienkiewicz, O.C. and Taylor, R.L. 1991, Finite Element

Method – Solid and Fluid Mechanics: Dynamics and

Nonlinearity, Vol. 2, McGraw-Hill: New York.

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